Metric dimension of Cayley digraphs of split metacyclic groups

被引：6

作者：

Abas, Marcel ^{[1
]}

Vetrik, Tomas ^{[2
]}

机构：

[1] Slovak Univ Technol Bratislava, Fac Mat Sci & Technol Trnava, Inst Appl Informat Automat & Math, Trnava, Slovakia

[2] Univ Free State, Dept Math & Appl Math, Bloemfontein, South Africa

来源：

THEORETICAL COMPUTER SCIENCE | 2020年 / 809卷

基金：

新加坡国家研究基金会;

关键词：

Metric dimension; Directed Cayley graph; Metacyclic group; Networks;

D O I：

10.1016/j.tcs.2019.11.025

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A directed Cayley graph Cay(Gamma, X) is specified by a group Gamma and an identity-free generating set X for this group. Vertices of Cay(Gamma, X) are elements of Gamma and there is a directed edge from a vertex u to a vertex v in Cay(Gamma, X) if and only if there is a generator x is an element of X such that ux = v. We study the metric dimension for the directed Cayley graphs Cay(Gamma(s) , {a,b}) of general split metacyclic groups, and present the exact values of the metric dimension for the special split metacyclic groups Gamma(s) = < a, b vertical bar a(n) = b(2s) =1, ba = a(-1)b >. (C) 2019 Elsevier B.V. All rights reserved.

引用

页码：61 / 72

页数：12

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